Related papers: Stochastic Games on Large Sparse Graphs

We study continuous stochastic games with heterogeneous mean field interactions and jumps on large networks and explore their limit counterparts. We introduce the graphon game model based on a controlled graphon mean field stochastic…

Coordination games have been of interest to game theorists, economists, and ecologists for many years to study such problems as the emergence of local conventions and the evolution of cooperative behavior. Approaches for understanding the…

Graphon games are a class of games with a continuum of agents, introduced to approximate the strategic interactions in large network games. The first result of this study is an equilibrium existence theorem in graphon games, under the same…

We consider a class of Nash games, termed as aggregative games, being played over a networked system. In an aggregative game, a player's objective is a function of the aggregate of all the players' decisions. Every player maintains an…

The mean field limit of large-population symmetric stochastic differential games is derived in a general setting, with and without common noise, on a finite time horizon. Minimal assumptions are imposed on equilibrium strategies, which may…

We investigate complexity issues related to pure Nash equilibria of strategic games. We show that, even in very restrictive settings, determining whether a game has a pure Nash Equilibrium is NP-hard, while deciding whether a game has a…

We consider a stochastic tournament game in which each player is rewarded based on her rank in terms of the completion time of her own task and is subject to cost of effort. When players are homogeneous and the rewards are purely rank…

Network congestion games are a convenient model for reasoning about routing problems in a network: agents have to move from a source to a target vertex while avoiding congestion, measured as a cost depending on the number of players using…

Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…

We study stochastic differential games with $N$ players, where interactions are determined by sequences of graphs in which the number of neighbours of each node remains bounded as $N$ grows, such as chain graphs or lattices. Our main goal…

We propose a novel neural network architecture, called Non-Trainable Modification (NTM), for computing Nash equilibria in stochastic differential games (SDGs) on graphs. These games model a broad class of graph-structured multi-agent…

Generating payoff matrices of normal-form games at random, we calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of $n$-player, $m$-strategy games. These are perfectly predictable as they must…

We analyse the typical structure of games in terms of the connectivity properties of their best-response graphs. Our central result shows that, among games that are `generic' (without indifferences) and that have a pure Nash equilibrium,…

In the context of large population symmetric games, approximate Nash equilibria are introduced through equilibrium solutions of the corresponding mean field game in the sense that the individual gain from optimal unilateral deviation under…

Strategic games admit a multi-graph representation, in which two kinds of relations, accessibility, and preferences, are used to describe how the players compare the possible outcomes. A category of games with a fixed set of players…

We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…

We prove that differential Nash equilibria are generic amongst local Nash equilibria in continuous zero-sum games. That is, there exists an open-dense subset of zero-sum games for which local Nash equilibria are non-degenerate differential…

This paper studies stochastic games on large graphs and their graphon limits. We propose a new formulation of graphon games based on a single typical player's label-state distribution. In contrast, other recently proposed models of graphon…

In the game theory literature, there appears to be little research on equilibrium selection for normal-form games with an infinite strategy space and discontinuous utility functions. Moreover, many existing selection methods are not…

Many important real-world settings contain multiple players interacting over an unknown duration with probabilistic state transitions, and are naturally modeled as stochastic games. Prior research on algorithms for stochastic games has…